Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
516 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22568797 | C2 | semidirect |
| 3. #22561946 | C2 | semidirect |
| 4. #22561944 | C2 | semidirect |
| 5. C2×#16863177 | C2 | semidirect |
| 6. #22558310 | C2 | semidirect |
| 7. C67×#1384 | C2 | semidirect |
| 13. #16863655 | C4 | semidirect |
| 14. #16863650 | C4 | semidirect |
| 33. C2×Dic268 | C2×C4 | semidirect |
| 35. C2×D536 | C2×C4 | semidirect |
| 60. #14523975 | D4 | semidirect |
| 72. #106×C67 | C2×C4 | semidirect |
| 73. #106×C67 | D4 | semidirect |
| 199. #1384 | D67 | semidirect |
| 200. C67 | #13008 | semidirect |
| 263. #106 | C4×D67 | semidirect |
| 264. #106 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569819 | 2 |
| #22568797 | 2 |
| #22561946 | 2 |
| #22561944 | 2 |
| C2×#16863177 | 2 |
| #22558310 | 2 |
| C67×#1384 | 2 |
| #13008 | 67 |